The conventional lighting fixtures of a ceiling fan are generally provided with a simple ON-OFF switch incapable of adjusting brightness of the ceiling fan lighting fixtures. The conventional ON-OFF switch can therefore result in inconvenience under the circumstances calling for various degrees of brightness of the lighting fixtures of the ceiling fan. A remote control device may be used to overcome such a problem as described above; nevertheless it is not economically feasible. An alternative way to control brightness of the lighting fixtures of a ceiling fan is to use a touch control device, which consists of a sensing piece capable of controlling brightness of the lighting fixtures of a ceiling fan upon being touched. This alternative way is in fact rather inconvenient. A cheaper way to control brightness of the lighting fixtures of a ceiling fan is to use a wall control device bearing a relatively low price tag and capable of an effective control of brightness of the lighting fixtures of a ceiling fan. However, the installation of the wall control device is time-consuming.